Componentwise stability of discrete-time interval bidirectional associative memorie

Abstract

The componentwise stability is a special type of asymptotic stability, which incorporates the positive invariance of certain time-dependent rectangular sets with respect to the state space trajectories. The paper develops the analysis of componentwise stability for discrete-time Bidirectional Associative Memory (BAM) neural networks with interval type parameters, providing criteria that allow monitoring the evolution of each state-space variable towards the equilibrium point. These criteria are formulated in terms of Schur stability of a test matrix adequately built from the intervals expressing the parameter uncertainties. Our approach represents a refinement of the classical results in stability theory, since the time-dependence of the considered invariant sets makes it possible to give a qualitative characterization of the dynamics at the level of the state vector components.